Question

$X$ and $Y$ together can do a work in $20$ days while $Y$ alone in $30$ days. They work together for two days and then $X$ goes away. In how many days will $Y$ finish the work ?

Answer 1

Given

X and Y can complete a work together in $20$ days.

$\frac{20}{x}+\frac{20}{y}=1$

Y alone can complete the work in $30$ days.

$\frac{20}{x}+\frac{20}{30}=1$

$\frac{20}{x}=\frac{1-2}{3}$

$\frac{20}{x}=\frac{1}{3}$

$x=60$ days.

$\frac{2}{60}+\frac{2}{30}+\frac{m}{30}=1$

$\frac{3}{30}+\frac{m}{30}=1$

$m+3=30$

$m=27$ days

Y finishes the remaining work in $27$ days.